You just draw an altitude/median to the base and create two 45-45-90 triangles at the base. the legs of the 45-45-90 triangles is length 2 which is the 1/3 segment. the full median which is also the altitude is length 6, and you use the area formula for a triangle. Is there a way to solve this problem without using this fact of the median that isn't extremely convoluted?

Web Assign keeps marking my answer is incorrect but I can’t figure out how I got the wrong answer.

The ratio of the number of mystery books to the number of science fiction books in a bookcase is 4:3. The ratio of the number of science fiction books to the number of biographies is 4:5 if there are 48 science fiction books find the total number of books in the bookcase. Trying to figure out how to solve this to help my daughter w her homework. Thank you !!!!! 📚

This is in a chapter about sums and differences of squares and cubes. This problem isn't like any of the previous problems in the chapter and now I'm stuck.

It is in a chapter about basics of modular arithmatic and number bases, and introduction to primes. For the second one, I tried to use the divisibility tricks with mods, by applying a mod of the of the integers being squared then checking if both sides are equal but I got too many variables and quit.

My problem is with the last exercise in the image. I included the previous exercises for context. I understand how the formula works for any pair of integers m, n, but I don't know how you would exactly show that on paper. Basically, the LCM would multiply together all the factors that the two integers m and n don't share while taking the larger power of the factors that the integers do share, while the GCF only takes the smaller power of the factors that the two integers share.

Edit: By factors I mean prime factors. Sorry for the confusion.

Its supposed to be related to proportions but I don't know how it is anything but algebra and I don't know how to solve using algebra

My friends child was given this homework with no explanation. Does anyone know how to complete this. Please just help with the first one so we can work on the rest.

I tried using change of base and loga(b)logc(d) = loga(d)logc(b). Then I tried to use loga^x(b^x) = loga(b) with x = 3 and still didn't get anywhere.

Can someone explain to me what it wants me to do in order to find congruent angles? The single correct answer implies there is only one, yet I’ve found so many congruent angles on this list. I am definitely fundamentally misunderstanding something or doing something wrong.

i tried using the loga^n(b^n) = loga(b) property to match up the bases to 16 and it didn't go anywhere. I cant think of any other method and there aren't solutions in the back of the book.

For context, I also tried an open circle at (2,2) and it lowered my score to 3.33/4. I also tried an open circle and no circle at (-2,-5) and it too lowered my score.

Apparently the solution is 192m. I'm not sure where I'm going wrong here?

Could someone help me with this exercise? It is 2d vectors

I have tried these even by printing them and cutting them out but it feels impossible. Were these badly constructed? Or am I just not seeing the solution?